 Relativity
Adam Hamilton
Archives
October 1, 2004
Whenever the word Relativity is uttered, most people immediately
think of last century's legendary physicist and genius Albert
Einstein.
Ninety-nine years ago Einstein
rocked the centuries-old foundation of Newtonian physics to its
very core. His Special Theory of Relativity, published in 1905,
claimed that Sir Isaac Newton's famous Three Laws of Motion were
only approximately correct, that they started crumbling when
velocities approached the speed of light. Einstein was right
of course, but his unconventional ideas shocked the scientific
world.
Interestingly, while the word
relativity is inexorably linked to Einstein now, the principle
bearing this name was actually introduced almost half a millennium
ago in Florence, a city state in what is now modern Italy. Celebrated
astronomer Galileo Galilei actually hatched the relativity idea
during his extensive studies of the heavenly bodies. While observing
planetary motion and celestial mechanics, Galileo pointed out
that motion was only meaningful in relation to something else,
a reference point.
In physics, all motion is relative.
If you are observing a moving object from a platform that is
also moving in the same direction and velocity, then there is
no apparent motion between you and the object.
For example, if you are reading
this essay near 40 degrees north or south latitude, like in the
central US, then both you and your computer or paper are careening
around near 800mph due to the Earth's rotation! Yet, since you
and everything in your world are all moving at the exact same
blistering 800mph speed, there is no apparent relative motion
from your perspective. All motion is relative!
It is in the spirit of this
pre-Einstein Galilean relativity that I would like to introduce
my idea of Technical Relativity. Just as motion in the heavenly
bodies is only relevant when considered in relative terms between
the observer and the observed, in the financial markets short-term
tradable price extremes are easiest to recognize relative to
recent precedent.
This whole Technical Relativity
thesis began gnawing at my skull about 18 months ago, as I studied
the famous VIX
implied volatility index in early 2003. As most speculators
know, VIX extreme highs virtually always mark major tradable
interim bottoms in the general stock markets. When a VIX extreme
high is reached, traders have a very high probability of winning
big if they immediately throw heavily long and buy index call
options.
It all sounds simple, buy stocks
when the VIX reaches an extreme high. After all, when the VIX
is high and fear abounds stocks should be low, and the entire
arts of investing and speculation can be summarized as Buy Low
Sell High. Yet, just as Pontius Pilate rhetorically asked Jesus
"What is truth?", speculators face similarly vexing
questions. We constantly wonder "What is high?" and
"What is low?". How do we know when a price is low
enough for us to buy or high enough for us to sell?
Unfortunately it is impossible
to emphatically answer these critical what-is-high and what-is-low
questions. We mere mortals cannot know the future before it happens,
and the markets are ultimately just a study in probabilities
anyway. But perhaps Technical Relativity can enable us to swing
these probabilities in our favor, to introduce trading discipline
to help increase our chances of buying when prices are truly
low and selling when prices are truly high.
Thus, this week I would like
to formally introduce my thesis of Technical Relativity. Like
Galilean relativity it is a simple idea that is easy to understand
when laid out logically. In the past year I have written about
relative studies countless times, but only tangentially in the
context of analyzing something else. I hope to dispel the mystery
and confusion surrounding Technical Relativity by fully explaining
it in logical context this week.
When Galileo gazed through
his ancient telescope at Jupiter, he realized that its apparent
motion was a product of both its own orbit as well as the orbit
of the very Earth on which he was standing. As you and I peer
through our computers today to attempt to decipher the gyrations
of the financial markets, we need to accept that our reference
points for buying and selling should not be static. Like the
Earth's motion relative to Jupiter, our vantage point for observing
trading opportunities is dynamic.
Thus a particular market price
may have been low or high in history, but that does not necessarily
make it relevant today. The Dow Jones Industrial Average topped
at the lofty height of 381.2 on September 3rd, 1929, a neck-snapping
all-time-record high at the time. Since the Dow had traded under 100
for decades before the infamous 1920s bubble, 381 seemed stellar
back in those days. Yet today with the Dow around 10k a level
of 381 seems unthinkably low, not high.
As investors and speculators
we can only decide that a particular market price is sufficiently
low enough to buy or high enough to sell in the context of recent
history. Lows and highs are not absolute, but totally relative.
What was high a decade ago in a given market is most likely very
different from what is considered high today or what will be
considered high a decade in the future. It's not only our trading
targets that are moving, like Jupiter's four largest moons which
Galileo discovered, but our very reference points for trading,
like Galileo's earthbound telescope.
As all this relativity stuff
percolated relentlessly between my ears early last year, I was
struggling with how we can use dynamic reference points as traders.
Without dynamic reference points, we get stuck using absolute
highs and lows that quickly become outdated as the markets evolve.
Yet, as soon as we get into relative reference points to define
tradable lows and highs, how do we remain objective? This paradox
sorely vexed me.
After far too much thought
about this puzzle a potential solution emerged, praise God!
What is a trading reference point that is not static, that moves
gradually over time to reflect new market realities, yet that
is totally objective and well defined? One answer is the 200-day
moving average of any price series! 200dmas are the perfect
happy medium between static reference points prone to obsolescence
and totally arbitrary dynamic reference points sans objectivity.
A 200dma is calculated by taking
today's closing price, adding the closing prices of the previous
199 trading days, and dividing by 200. Tomorrow, and on each
subsequent day, one new day's data is added while the oldest
day's close is dropped off. Thus this constantly rolling 200dma
provides an ideal objective dynamic reference point that only
considers the last 200 trading days' action, roughly 10 calendar
months.
Now calculating 200dmas way
back in Galileo's time would have been a hideous exercise in
self torment. Can you imagine writing out 200 closing prices
in longhand, adding them up, dividing by 200, and then repeating
this exercise over and over every single trading day? Ouch,
I think I would have fallen on my sword first before manually
calculating 200dmas!
Thankfully though in our modern
computer age common spreadsheet software like Excel can effortlessly
calculate endless 200dmas in a fraction of a second. Hence this
analysis is easily accessible and replicable by everyone today.
200dmas have long been considered
one of the most important lines in all of technical analysis,
largely for two reasons. First, 200dmas tend to run parallel
with the secular, or long-term, trend in force in any market.
Thus a 200dma is like a big arrow pointing in the direction that
a market is heading. Second, 200dmas tend to form the most foundational
bull-market support or bear-market resistance of a secular trend.
Short countertrend pullbacks (in a bull) or bear-market rallies
(in a bear) tend to end at the 200dma.
This tendency is very easy
to see in any graph of a secular trend. While my Technical Relativity
thesis is totally neutral and can be applied to any market, I
chose to use gold in these particular examples. Gold is a market
near and dear to my own heart that I have written extensively
about in recent years, so I am intimately familiar with it.
In addition, its current secular
bull market is textbook perfect for illustrating the magic
of the mighty 200-day moving average.
Thus our first graph shows
gold's current secular bull to date, as well as its 200dma.
Way back in April 2001, which
feels about as ancient as Galileo these days, gold stealthily
carved a long-term bottom just above $250. In the subsequent
three years it marched relentlessly higher to achieve its current
bull-to-date highs just above $425. As such, after more than
three years gold is indisputably in a secular bull market.
Gold's black 200dma above,
just like it ought to, acts as a big arrow running parallel with
gold's primary trend. If you drew a simple linear trend channel
to envelope the gold price in the last few years, gold's 200dma
would run along with it roughly parallel like a third railroad
track. Because 200dmas distill about 10 months worth of trading
action they deftly filter out all the short-term market noise
and point out the true underlying trend of any price.
The whole thesis of Technical
Relativity rests on the second great attribute of 200dmas though,
their tendency to act as the major support in a bull market or
major resistance in a
bear market. If you carefully examine the price data above,
you will note that gold's inevitable countertrend pullbacks and
corrections tend to bounce higher right near its 200dma. This
is why investors and speculators have often viewed the 200dma
as the most important technical line.
Why is this phenomenon universal
across all markets? The very mathematical nature of a 200dma
makes it so. Since the 200dma considers today's close along with
the preceding 199 days' closes, it tends to lag actual prices.
200dmas are constantly struggling to catch up with secular trends.
In a very real sense, it is not the price reverting to the 200dma
that is the noteworthy technical event, but the price moving
countertrend long enough to give the 200dma time to catch up.
Stated another way, the mathematical
interaction of an ongoing secular trend and its 200dma is a constant
duel between convergence and divergence. When speculators get
excited and bid up prices, a price pulls away and diverges from
its 200dma. At some point though, greed waxes too extreme and
a countertrend reversion is due. At this point a price pulls
back and converges with its 200dma. Like a giant sine wave, a
trending market constantly sprints away from and then returns
to revisit its trailing 200dma.
As investors and speculators,
we want to consider trading when these price and 200dma convergences
and divergences grow extreme. In a bull market we want to buy
near 200dma convergences and sell near 200dma divergences. In
a bear market the opposite approach is in order, selling near
200dma convergences and buying near 200dma divergences. The gold
chart above beautifully illustrates this timeless principle.
So far in this gold bull to
date, there have been five interim lows that were ideal points
to buy and four interim highs that were ideal points to sell.
All these buy-low convergence points are labeled in green while
the sell-high divergence points are labeled in red. Notice that
all of the green buy-low points are at or near the black 200dma
line, while all of the red sell-high points are far away from
the 200dma.
So if you are a speculator
who wants to buy low and sell high, all you need to do in a secular
bull market is buy when a price nears its 200dma and prepare
to sell when it stretches too far away from its 200dma. If you
are an investor who wants to buy low and hold, you should only
consider buying when a price nears its 200dma. If you buy when
a price diverges from its 200dma, then odds are you are not getting
the best possible price.
Thus the perpetual interaction
between a price in a secular trend and its 200dma is of paramount
importance for both investors and speculators to monitor. We
can better gauge opportunities to buy low and sell high by observing
a price relative to its 200dma. The 200dma provides a relative
reference point that gradually follows any market price yet remains
perfectly objective since it is a mathematical construct totally
devoid of emotional bias.
Now that the immense power
of the 200dmas is apparent, another problem arises. While hindsight
is 20/20 and eyeballing a graph illustrates the principle of
200dma convergences and divergences as opportune moments to trade,
we need a tool to help us recognize these in real-time. After
all, when we hit one of these interim lows and highs like the
ones shown above we need to be trading right now, not waiting
a few months while the great opportunity passes us by.
In addition, we need a precise
way to quantify these 200dma convergences and divergences. Due
to the nature of graphs and price percentage changes off of varying
bases, what our eye sees is often deceiving. To illustrate this,
please check out points 2, 6, and 8 above. At which point do
you think gold is farthest above its 200dma? Visually, my eyes
tell me that point 2 is the least far above its 200dma while
point 8 is the most far above its 200dma. But my eyes deceive
me.
The true answer is revealed
by the black numbers above, which quantify where gold hit an
interim top or bottom relative to its 200dma. At point 2 gold
topped $38 above its 200dma, $38 again at point 6, and $41 at
point 8. Thus these distances, in absolute terms, are essentially
the same! If we can only rely on visual cues on a graph, we
are stuck with distortions due to changing bases (a rising 200dma)
and true distances are tough to gauge.
When the power of trading on
200dma convergence-and-divergence extremes is combined with the
problem of precisely quantifying and recognizing these very extremes,
the Technical Relativity thesis is born. Relativity creates a
simple objective tool that empowers traders to recognize tradable
200dma extremes while totally eliminating the visual distortions
and emotional bias inherent in chart analysis.
Rather than relying on absolute
prices such as gold's graphed above, Technical Relativity considers
prices in relation to their 200dma. The 200dma becomes the gradually
moving reference point, like the Earth was for Galileo's telescope.
Thus we no longer care that gold is $20, $40, or $60 above its
200dma. Instead we are concerned of at what multiple of its 200dma
that gold happens to be trading at the moment.
Computing a Technical Relativity
number is exceedingly easy. The simple formula is closing price
divided by its current 200dma. So if gold was trading at $440
and its 200dma was hovering near $400, then Relative Gold, or
rGold in shorthand, would be $440 divided by $400, or 1.1. An
rGold reading of 1.1 tells us that gold is currently trading
at 1.1x, or 110% of, its 200dma.
Thinking of a market price
in terms of a multiple to its 200dma deftly kills multiple technical
problems with one stone. Because we are now talking in multiples
and percentages, the base level no longer matters. Whether gold
is trading $20 above its 200dma at $220 or $100 above its 200dma
at $1100, it still has the same relative level of 1.1 in both
cases. Technical Relativity eliminates the distortion inherent
in using absolute numbers as compared to a constantly changing
base over time.
In order to visualize why a
relativity graph looks like it does, imagine if the black 200dma
line above was flattened into a horizontal axis, and gold was
flattened as appropriate right along with it. Rather than rising,
the 200dma would always be constant at 1.0, a perfectly flat
horizontal line regardless of gold's absolute price. And oscillating
around this 1.0 line representing gold trading at a multiple
of its 200dma, the rGold number would meander.
When gold was trading above
its 200dma, the relativity reading would be greater than 1.0.
When gold was trading below its 200dma, the relativity reading
would be less than 1.0. And when gold hit its 200dma, the rGold
reading would be exactly 1.0. Simple, yet powerful, stuff.
Our next graph this week undertakes
this flattening operation just described. The absolute gold numbers
from the first graph above are moved to the right axis, while
the left axis notes relative gold. The black 200dma line slaved
to the right axis evolves into the flat 1.0 rGold centerline
on the left axis. And the wildly oscillating blue gold line on
the right axis becomes the flattened red multiple of gold's 200dma
on the left axis.
Behold Technical Relativity!
I hope Galileo can forgive me for shamelessly appropriating
his wonderful term.
Just like this Relative Gold
graph, a Technical Relativity indicator effectively flattens
a price's 200dma along the 1.0 line and then shows the price
as a multiple of that 200dma. This simple conversion calculated
by dividing a price by its 200dma eliminates the distortion and
skew always inherent in using absolute prices to make buying
and selling decisions over time.
Now, regardless of the absolute
level of gold, we have a constant-percentage comparison of it
relative to its key 200dma support over time. Whether gold is
trading at $400 or $4000 makes no difference in a relativity
graph, if rGold is at 1.10 then gold is trading at 110% of its
200dma regardless of its 200dma's base. This tool provides an
outstanding relative reference point for us to consider in determining
whether the gold price happens to be low or high on any particular
day.
All nine points labeled above
correspond with the first graph, but this time they include the
rGold reading. The second number below rGold is the number of
days between rGold's top or bottom and the actual top and bottom
in gold. In only two cases above did the rGold turning point
vary from that of gold itself.
Interestingly, however, the
gold price only moved by 2.7% in the first case at point 3 and
0.2% in the second case at point 8 between the rGold interim
extreme and the actual gold interim extreme. Thus, even in peculiar
situations where a Relativity extreme doesn't coincide exactly
with an actual price extreme, the percentage difference over
this period of time is usually trivial. In general, relativity
extremes mark true price extremes very accurately.
The beauty of a relative indicator
is it gives us a range of interest over time to guide our actual
trades, and this range is generally fairly consistent. A couple
examples really help illustrate this key point.
First, please consider points
5 and 9 on the buy side. As the first graph showed, gold traded
at $323 and $374 at these points respectively. Both points marked
fantastic moments to buy gold, but the actual gold price at which
these buy opportunities triggered varied dramatically. At what
gold price should traders buy in the future? Technical Relativity
solves this puzzle as it considers gold as a constant multiple
of its 200dma.
At point 5 rGold traded down
to 0.981, under 1.0 which marks gold's 200dma. At point 9 rGold
traded even lower, down to 0.953. Both of these rGold buying
opportunities, even though gold itself was at very different
levels, witnessed sub-1.0 rGold readings. In fact, if you look
at all five odd-numbered buying opportunities above, you will
note that rGold was always right around 1.0 or so to mark all
of the greatest buying opportunities in this entire bull market
to date. So why not buy next time rGold trades around 1.0 or
so?
The sell signals on top work
the same way. The gold sell at point 2 happened at $327 but the
gold sell at point 8 happened at $427. While a vast gulf separates
these actual prices, the relative levels of gold were 1.130 and
1.156 respectively during both of these ideal moments to sell.
Gold had advanced too far away from its 200dma so a divergence
was in order to bring this ratio back into line in both cases.
So why not sell next time rGold heads north of 1.14ish or so?
Technical Relativity helps
precisely quantify a price's typical extremes relative to its
200dma over time, and as investors and speculators we can use
these past extremes to help us identify future trading opportunities
in real-time. We don't have to worry about whether a price is
absolutely low or high when we can view prices as relatively
low or high as compared to their key 200dmas.
Now after a trend has been
running for a couple years, like gold's above, we can even use
the previous extremes to define a potential trading range to
watch for in the future. There are a couple steps to take in
finding and defining one of these relative trading ranges.
First, it is useful to consider
an entire relative range in percentage terms. To start, build
a graph like this one running back two or three years. In general
I think relativity ranges should encompass two to three years
of data, but not too much more. We want our relativity indicators
to stay current and reflect today's market conditions, so it
is important to drop off old data periodically when considering
extremes. Two to three years is just about right.
With these few years of data,
find the highest and lowest relative readings. In gold's case
above the highest the Ancient Metal of Kings has climbed relative
to its 200dma was to 1.184x at point 4 in early 2003. The lowest
gold has traded since its bull market began in April 2001 occurred
just this past May at an rGold reading of 0.953. If we subtract
this low from this high we get a max relative range to date of
0.231.
Now, as a general principle,
a price cannot be extreme very often. If we consider a one-hundred
percent range, it is probably not a problem to only consider
the top 10% and bottom 10% as "extreme". This leaves
the middle 80% to be considered as "normal" price movements.
We are only interested in these relativity indicators when they
approach the top or bottom 10% or so of their ranges.
In gold's case 10% of its 0.231
relative range is 0.0231. This 10% added to the bottom of the
range (0.953) and subtracted from the top (1.184) yields us an
initial relativity range of 0.976 to 1.161. Now if you look at
the graph above, rGold only traded out of this range twice, once
to the upside and once to the downside. With 9 major turning
points and 2 extremes, this works pretty well as considered in
the lower 10% extreme, 80% normal, and upper 10% extreme paradigm.
This brings us to our second
step in defining these relative trading ranges. In some cases,
there can be an outlier that skews this range. This has happened
a little bit in gold, with the high and low readings above both
a bit higher and lower than its general high and low relative
readings. If you draw two lines in the graph above intersecting
the rGold levels of 0.976 and 1.161, they only have one real-world
intercept each. I believe this is insufficient for a trading
indicator.
In these cases where there
is only one intercept on the top and bottom with the 10%, 80%,
10% model, it is best to rein in the relativity range so there
are at least two intercepts each on the top and bottom. This
helps prevent outliers from skewing the relativity range beyond
what we might expect to see in the future. Using this farther
refinement, I defined an rGold range of interest of <0.990
to >1.140 based on the data above. These buy and sell zones
are shaded in this graph.
When gold approaches a relative
reading of 0.990 or less on the low side, it is time to consider
buying with reckless abandon as long as you think its secular
bull market remains in force. Similarly, if you are a speculator,
whenever rGold gets near or above 1.140 it is time to consider
selling, going neutral, or even shorting. Gold has intersected
these levels twice at both the top and bottom of its relative
band in recent years, so this range looks pretty solid.
An important caveat to consider
when using relativity ranges as trading tools is that the old
warnings that the markets are nothing more than a game of probabilities
definitely applies. The farther away from its 200dma a price
stretches, the more likely it is to revert back dramatically.
But there are no magic levels. A price can easily turn around
before or after a relativity band is reached. Relativity is another
valuable tool to help us understand when high-probability-for-success
trades are possible, but it cannot forecast the future. It is
no crystal ball.
And while I chose to use gold
in this example today, Technical Relativity is a generic tool
that can be applied to any trending market. At Zeal, between
our published work and unpublished internal research, we have
run relativity analyses on all of the major US stock indices,
stock ETFs, the implied volatility indices, a bunch of commodities,
various currencies, sector indices, and even individual stocks.
Any trending price is a potential candidate for relativity analysis.
In fact in the brand new October
Zeal Intelligence
monthly newsletter just published for our subscribers,
we totally revamped our various trading indicators including
all the relativity ones. New indicators have been added and existing
indicators have been totally recalibrated. While our primary
focus continues to be on the immensely profitable precious-metals
arena for most of our investments and speculations these days,
we continue to watch other markets as well and are ready to strike
fast when great opportunities arise.
Please subscribe
today to see these 17 new and updated trading indicators
and learn how we use them to launch high-probability-for-success
trades as appropriate in the coming months.
Just like Galileo Galilei declaring
that all planetary motion was only relevant on a relative basis,
that there were no absolute celestial reference points, I believe
that investing and speculation can benefit greatly from a similar
relative focus. Observing prices relative to their 200dmas provides
a sound measuring point for our modern financial explorations
today.
Technical Relativity combines
the timeless principle of 200dma convergences and divergences
as major trading opportunities with an absolutely objective way
to measure and compare these extremes over time. After a trending
market establishes an effective range, investors and speculators
would do well to monitor and heed these relativity signals.
October 1, 2004
Adam Hamilton, CPA
email:
zelotes@zealllc.com
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